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Computing hour angle from mean equinox at beginning of nearest Besselian year to Greenwich meridian for RTCC predictor for Apollo Missions E, F, and G
Computer programs and predictor displays for solving air traffic control problems
Predictor-corrector schemes are discussed for the numerical integration of initial value problems by computer. Descloux formulas, which are considered modified Nordsieck formulas are studied because of their desirable stability and truncation properties along with the standard Nordsieck formulas. The stability of Nordsieck and modified Nordsieck algorithms are computed, and the results are graphed. Test problems are included as examples for comparing the efficiency of the algorithms.
The requirements and processing logic for the LACIE Error Model program (LEM) are described. This program is an integral part of the Large Area Crop Inventory Experiment (LACIE) system. LEM is that portion of the LPP (LACIE Performance Predictor) which simulates the sample segment classification, strata yield estimation, and production aggregation. LEM controls repetitive Monte Carlo trials based on input error distributions to obtain statistical estimates of the wheat area, yield, and production at different levels of aggregation. LEM interfaces with the rest of the LPP through a set of data files.
The LACIE Performance Predictor (LPP) is a computer simulation of the LACIE process for predicting worldwide wheat production. The simulation provides for the introduction of various errors into the system and provides estimates based on these errors, thus allowing the user to determine the impact of selected error sources. The FOC LPP simulates the acquisition of the sample segment data by the LANDSAT Satellite (DAPTS), the classification of the agricultural area within the sample segment (CAMS), the estimation of the wheat yield (YES), and the production estimation and aggregation (CAS). These elements include data acquisition characteristics, environmental conditions, classification algorithms, the LACIE aggregation and data adjustment procedures. The operational structure for simulating these elements consists of the following key programs: (1) LACIE Utility Maintenance Process, (2) System Error Executive, (3) Ephemeris Generator, (4) Access Generator, (5) Acquisition Selector, (6) LACIE Error Model (LEM), and (7) Post Processor.
Two types of parameters are computed and mapped for use in assessing their individual merits as predictors of occurrence and severity of thunderstorms. The first group is comprised of equivalent potential temperature, potential temperature, water vapor mixing ratio, and wind speed. Equivalent potential temperature maxima and strong gradients of equivalent potential temperature at the surface correlate well with regions of thunderstorm activity. The second type, comprised of the energy index, shear index, and energy shear index, incorporates some model dynamics of thunderstorms, including nonthermodynamic forcing. The energy shear index is found to improve prediction of tornadic and high-wind situations slightly better than other indices. It is concluded that further development and refinement of nonthermodynamic aspects of predictive indices are definitely warranted.
The documentation and user's guide for the Analytical Satellite Orbit Predictor (ASOP) computer program is presented. The ASOP is based on mathematical methods that represent a new state-of-the-art for rapid orbit computation techniques. It is intended to be used for computation of near-earth orbits including those of the shuttle/orbiter and its payloads.
The documentation and user's guide are presented for the analytical satellite orbit predictor computer program which is intended to be used for computation of near-earth orbits including those of the shuttle orbiter and its payloads. The Poincare-Similar elements used make it possible to compute near-earth orbits to within an accuracy of a few meters. Recursive equations are used instead of complicated formulas. Execution time is on the order of a few milliseconds.
A multiphase selfadaptive predictor corrector type algorithm was developed. This algorithm enables the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as pro/post buckling behavior. The strategy involves three main phases: (1) the use of a warpable hyperelliptic constraint surface which serves to upperbound dependent iterate excursions during successive incremental Newton Ramphson (INR) type iterations; (20 uses an energy constraint to scale the generation of successive iterates so as to maintain the appropriate form of local convergence behavior; (3) the use of quality of convergence checks which enable various self adaptive modifications of the algorithmic structure when necessary. The restructuring is achieved by tightening various conditioning parameters as well as switch to different algorithmic levels to improve the convergence process. The capabilities of the procedure to handle various types of static nonlinear structural behavior are illustrated.
An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.
Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.
The design of the Hybrid Automated Reliability Predictor (HARP), now under development at Duke University, is presented. The HARP approach to reliability prediction is characterized by a decomposition of the overall model into fault-occurrence and fault-handling sub-models. The fault-occurrence model is a non-homogeneous Markov chain which is solved analytically, while the fault-handling model is a Petri Net which is simulated. HARP provides automated analysis of sensitivity to uncertainties in the input parameters and in the initial state specifications. It then produces a predicted reliability band as a function of mission time, as well as estimates of the improvement (narrowing of the band) to be gained by a specified amount of reduction in uncertainty.
An adaptive numeric predictor-corrector guidance is developed for atmospheric entry vehicles which utilize lift to achieve maximum footprint capability. Applicability of the guidance design to vehicles with a wide range of performance capabilities is desired so as to reduce the need for algorithm redesign with each new vehicle. Adaptability is desired to minimize mission-specific analysis and planning. The guidance algorithm motivation and design are presented. Performance is assessed for application of the algorithm to the NASA Entry Research Vehicle (ERV). The dispersions the guidance must be designed to handle are presented. The achievable operational footprint for expected worst-case dispersions is presented. The algorithm performs excellently for the expected dispersions and captures most of the achievable footprint.
By using Von Zeipel's generating function procedure the perturbing earth gravitational potential is averaged with respect to the fast variable (mean anomaly) and a set of 'fictitous' mean orbital elements which can be used as a long-term satellite orbit predictor is obtained. The set of elements is shown to be a function of the nonlinear square of the second zonal harmonic coefficient. It is found that the long-term orbit prediction using the 'fictitous' mean elements is as accurate as that using the osculating elements, but has a computing speed about two orders of magnitude faster. For short-term orbit predictions, the osculating elements approach must be used.
A three-degree-of-freedom predictor-corrector guidance algorithm has been developed specifically for use in high-energy aerobraking performance evaluations. The present study reports on both the development and capabilities of this guidance algorithm to the design of manned Mars aero-braking vehicles. Atmospheric simulations are performed to demonstrate the applicability of this algorithm and to evaluate the effect of atmospheric uncertainties upon the mission requirements. The off-nominal conditions simulated result from atmospheric density and aerodynamic characteristic mispredictions. The guidance algorithm is also used to provide relief from the high deceleration levels typically encountered in a high-energy aerobraking mission profile. Through this analysis, bank-angle modulation is shown to be an effective means of providing deceleration relief. Furthermore, the capability of the guidance algorithm to manage off-nominal vehicle aerodynamic and atmospheric density variations is demonstrated.
The Hybrid Automated Reliability Predictor (HARP) integrated reliability (HiREL) workstation tool system marks another step toward the goal of producing a totally integrated computer aided design (CAD) workstation design capability. Since a reliability engineer must generally graphically represent a reliability model before he can solve it, the use of a graphical input description language increases productivity and decreases the incidence of error. The captured image displayed on a cathode ray tube (CRT) screen serves as a documented copy of the model and provides the data for automatic input to the HARP reliability model solver. The introduction of dependency gates to a fault tree notation allows the modeling of very large fault tolerant system models using a concise and visually recognizable and familiar graphical language. In addition to aiding in the validation of the reliability model, the concise graphical representation presents company management, regulatory agencies, and company customers a means of expressing a complex model that is readily understandable. The graphical postprocessor computer program HARPO (HARP Output) makes it possible for reliability engineers to quickly analyze huge amounts of reliability/availability data to observe trends due to exploratory design changes.
A new algorithm for identifying and characterizing vortices in complex flows is presented. The scheme uses both the vorticity and pressure fields. A skeleton line along the center of a vortex is produced by a two-step predictor-corrector scheme. The technique uses the vector field to move in the direction of the skeleton line and the scalar field to correct the location in the plane perpendicular to the skeleton line. A general vortex cross section can be concisely defined with five parameters at each point along the skeleton line. The details of the method and examples of its use are discussed.
The Hybrid Automated Reliability Predictor (HARP) integrated Reliability (HiRel) tool system for reliability/availability prediction offers a toolbox of integrated reliability/availability programs that can be used to customize the user's application in a workstation or nonworkstation environment. HiRel consists of interactive graphical input/output programs and four reliability/availability modeling engines that provide analytical and simulative solutions to a wide host of highly reliable fault-tolerant system architectures and is also applicable to electronic systems in general. The tool system was designed at the outset to be compatible with most computing platforms and operating systems, and some programs have been beta tested within the aerospace community for over 8 years. This document is a user's guide for the HiRel graphical preprocessor Graphics Oriented (GO) program. GO is a graphical user interface for the HARP engine that enables the drawing of reliability/availability models on a monitor. A mouse is used to select fault tree gates or Markov graphical symbols from a menu for drawing.